Classical Möbius-ring resonators exhibit fermion-boson rotational symmetry Academic Article uri icon


MeSH Major

  • Models, Theoretical
  • Radio Waves


  • The behavior of coupled harmonic oscillators in systems with specified boundary conditions is typically characterized by resonances whose frequency spectra represent harmonics according to properties of the individual oscillators, the interactions between them, and the overall symmetry of the system. Here it is demonstrated that classical one- and two-dimensional radio frequency resonators constrained to a Möbius topology are the formal partners of cylindrical ring resonators, and specifically give rise to half-integral harmonic excitations that are orthogonal to the integral excitations of a ring. In particular, the half-integral harmonics are formally invariant under rotations at a minimum of 4pi rather than 2pi rad, in analogy to the rotational symmetry of fermions in quantum mechanics. The results offer a pathway for discovery in other physical systems as well as the design of novel materials and electronic instrumentation.

publication date

  • December 8, 2008



  • Academic Article



  • eng

Digital Object Identifier (DOI)

  • 10.1103/PhysRevLett.101.247701

PubMed ID

  • 19113667

Additional Document Info

start page

  • 247701


  • 101


  • 24